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Derivatives of order upto two MCQs for JEE

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Part of Limit, Continuity and Differentiability in JEE Main Mathematics.

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Q1MathsUnit 7: Limit, Continuity and Differentiability
Assertion(A): Let f(x)\boldsymbol{f}(\boldsymbol{x}) be twice differentiable function such that f′′(x)=−f(x)\boldsymbol{f}^{\prime \prime}(\boldsymbol{x})=-\boldsymbol{f}(\boldsymbol{x}) and f′(x)=g(x).\boldsymbol{f}^{\prime}(\boldsymbol{x})=\boldsymbol{g}(\boldsymbol{x}) . If h(x)=[f(x)]2+[g(x)]2\boldsymbol{h}(\boldsymbol{x})=[\boldsymbol{f}(\boldsymbol{x})]^{2}+[\boldsymbol{g}(\boldsymbol{x})]^{2} and h(1)=8\boldsymbol{h}(\mathbf{1})=\mathbf{8} then⁡h(2)=8\operatorname{then} h(2)=8 Reason (R): Derivative of a constant function is zero.

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